Freiman's theorem in an arbitrary abelian group

BJ Green, IZ Ruzsa

Research output: Contribution to journalArticle (Academic Journal)peer-review

94 Citations (Scopus)


A famous result of Freiman describes the structure of finite sets A {subseteq} Z with small doubling property. If |A + A| ≤ K|A|, then A is contained within a multidimensional arithmetic progression of dimension d(K) and size f(K)|A|. Here we prove an analogous statement valid for subsets of an arbitrary abelian group.
Translated title of the contributionFreiman's theorem in an arbitrary abelian group
Original languageEnglish
Pages (from-to)163 - 175
Number of pages13
JournalJournal of the London Mathematical Society
Volume75 (1)
Publication statusPublished - Feb 2007

Bibliographical note

Publisher: Oxford University Press


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